Some remarks on the volume of log varieties
Algebraic Geometry
2020-04-22 v3
Abstract
In this note, using methods introduced by Hacon, McKernan and Xu, we study the accumulation points of volumes of varieties of log general type. First, we show that, if the set of boundary coefficients is DCC, closed under limits and contains 1, then also the corresponding set of volumes is DCC and closed under limits. Then, we consider the case of -log canonical varieties, for . In this situation, we prove that, if is finite, then the corresponding set of volumes is discrete.
Cite
@article{arxiv.1804.10971,
title = {Some remarks on the volume of log varieties},
author = {Stefano Filipazzi},
journal= {arXiv preprint arXiv:1804.10971},
year = {2020}
}
Comments
Fixed some typos (including an inequality in the statement of Theorem 1.3). arXiv admin note: text overlap with arXiv:1706.09913